This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327472 #8 Sep 22 2023 01:58:47
%S A327472 1,0,0,1,2,5,6,13,16,25,34,54,56,99,121,154,201,295,324,488,541,725,
%T A327472 957,1253,1292,1892,2356,2813,3378,4563,4838,6840,7686,9600,12076,
%U A327472 14180,15445,21635,25627,29790,33309,44581,48486,63259,70699,82102,104553,124752
%N A327472 Number of integer partitions of n not containing their mean.
%e A327472 The a(3) = 1 through a(8) = 16 partitions not containing their mean:
%e A327472 (21) (31) (32) (42) (43) (53)
%e A327472 (211) (41) (51) (52) (62)
%e A327472 (221) (411) (61) (71)
%e A327472 (311) (2211) (322) (332)
%e A327472 (2111) (3111) (331) (422)
%e A327472 (21111) (421) (431)
%e A327472 (511) (521)
%e A327472 (2221) (611)
%e A327472 (3211) (3311)
%e A327472 (4111) (5111)
%e A327472 (22111) (22211)
%e A327472 (31111) (32111)
%e A327472 (211111) (41111)
%e A327472 (221111)
%e A327472 (311111)
%e A327472 (2111111)
%t A327472 Table[Length[Select[IntegerPartitions[n],!MemberQ[#,Mean[#]]&]],{n,0,20}]
%o A327472 (Python)
%o A327472 from sympy.utilities.iterables import partitions
%o A327472 def A327472(n): return sum(1 for s,p in partitions(n,size=True) if n%s or n//s not in p) if n else 1 # _Chai Wah Wu_, Sep 21 2023
%Y A327472 The Heinz numbers of these partitions are A327476.
%Y A327472 Partitions with their mean are A237984.
%Y A327472 Subsets without their mean are A327471.
%Y A327472 Subsets with n but without their mean are A327477.
%Y A327472 Strict partitions without their mean are A240851.
%Y A327472 Cf. A007865, A067538, A067538, A102627, A114639, A324756, A327473.
%K A327472 nonn
%O A327472 0,5
%A A327472 _Gus Wiseman_, Sep 13 2019